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Line–line intersection. In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line. Distinguishing these cases and finding the intersection have uses, for example, in computer graphics, motion planning, and collision detection . In three-dimensional Euclidean geometry, if two lines are not in ...
Intersection (geometry) The red dot represents the point at which the two lines intersect. In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the line–line intersection between two distinct lines, which either is one ...
Mach bands can also appear when there is a discontinuity in the derivative of a gradient, a visual effect common when intensities are linearly interpolated such as in Gouraud shading. Computer image processing systems use edge-detection in a way analogous to the brain, using unsharp masking to clarify edges in photos for example.
In geometry, the parallel postulate, also called Euclid 's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry: If a line segment intersects two straight lines forming two interior angles on the same side that are less than two right ...
The three possible line-sphere intersections: 1. No intersection. 2. Point intersection. 3. Two point intersection. In analytic geometry, a line and a sphere can intersect in three ways: Intersection in two points. Methods for distinguishing these cases, and determining the coordinates for the points in the latter cases, are useful in a number ...
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Angle. A green angle formed by two red rays on the Cartesian coordinate system. In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. [1] Angles formed by two rays are also known as plane angles as they lie in the plane that contains the rays.
In geometry, two lines and are antiparallel with respect to a given line if they each make congruent angles with in opposite senses. More generally, lines and are antiparallel with respect to another pair of lines and if they are antiparallel with respect to the angle bisector of and. In any cyclic quadrilateral, any two opposite sides are ...